Question

By the end of the first century bce the romans had perfected which architectural innovation

Answer 1

The dome

The Pantheon is a famous Roman dome built in the first century BCE.  Marcus Agrippa commissioned the building after participating in Rome's victory at the Battle of Actium.  It was the largest dome in the world until 1881.

Domes were built in cities beyond Rome itself also, such the Temple of Mercury, the Temple of Venus, and the Temple of Diana, all located in Baiae, on the shore of the Gulf of Naples.